I'd start with wahealthplanfinder.org. You can plug in your family info and get an idea of costs. The info is geared toward the low-income segment, so if your part-time work doesn't qualify you at least you'll get some ideas of who in your area provides coverage.
Once you get into various plans and options, there are several terms to understand: deductibles, copays, coinsurance, etc. I don't have a good resource handy for that (hopefully someone else does). Your best value should be a high-deductible plan with HSA.
Of course, your individual family situation (existing conditions/meds, children on your plan, etc) will potentially change things. So look at today and also how it might be different post-FI.